Second order subexponential distributions

Subexponential Distributions

We survey the properties and uses of the class of subexponential probability distributions, paying particular attention to their use in modelling heavy-tailed data such as occurs in insurance and queueing applications. We give a detailed summary of the core theory and discuss subexponen-tiality in various contexts including extremes, random walks and L evy processes with negative drift, and sum...

Resource Sharing with Subexponential Distributions

We investigate the distribution of the waiting time V in an M/G/1 processor sharing queue with traffic intensity ρ < 1. This queue represents a baseline model for evaluating efficient and fair network resource sharing algorithms, e.g. TCP flow control. When the distribution of job size B belongs to a class of subexponential distributions with tails heavier than e− √ , it is shown that as x → ∞ ...

Convolutions of long-tailed and subexponential distributions

We study convolutions of long-tailed and subexponential distributions (probability measures), and more general finite measures, on the real line. Our aim is to prove some important new results, and to do so through a simple, coherent and systematic approach. It turns out that all the standard properties of such convolutions are then obtained as easy consequences of these results. Thus we also h...

Telecommunication Traffic, Queueing Models, and Subexponential Distributions

Higher-order Expansions for Compound Distributions and Ruin Probabilities with Subexponential Claims

Let Xi (i = 1, 2, . . .) be a sequence of subexponential positive independent and identically distributed random variables. In this paper we offer two alternative approaches to obtain higher-order expansions of the tail of ∑n i=1 Xi and subsequently for ruin probabilities in renewal risk models with claim sizes Xi. In particular, these emphasize the importance of the term P( ∑n i=1 Xi > s,max(X...